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TRANSCRIPT
DIRECT DARK MATTER SEARCHES AND
FINE-TUNING IN SUPERSYMMETRY
Bibhushan Shakya
Cornell University
LEPP Particle Theory Seminar
November 4, 2011
Based on arXiv:1107.5048 with Maxim Perelstein
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Several direct detection experiments searching for
dark matter; exciting times!
Recently beginning to probe interesting regions where
SUSY predicts signals
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Future upgrades will probe even lower cross sections
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Uncertainties in Direct Detection Experiments
! Local dark matter density
! Velocity distribution
! Isospin symmetry of WIMP-nucleon couplings
! Nuclear formfactors (esp. that of the strange quark)
! Channeling…
Will not discuss these further,
assume they are known and properly incorporated,
bound on direct detection cross section as a function of
WIMP mass as starting point
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Interpreting results in the context of MSSM
! Large number of free parameters (>100), allowed ranges highly
uncertain
! Reduce parameter space via specific assumptions that relate
otherwise independent parameters, e.g. high scale unification,
specific model of SUSY breaking
! E.g. mSUGRA has only 5 parameters (but serious issues with
FCNCs)
! Use results of direct detection to make exclusion plots on
combinations of free parameters (while assuming specific values
for free parameters not on the plot)
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Bounds on parameter combinationsNull results
hep-ph 1104.3572
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What is the most general take-away message ??
Bounds on parameter combinationsNull results
hep-ph 1104.3572
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A meaningful measure:
Fine-tuning
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A meaningful measure:
Fine-tuning
The Question
In generic supersymmetry models, can one
naturally get points that evade current and
future direct detection constraints, without
needing to fine-tune parameters?
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Quantifying (EWSB) Fine-tuning
• In EW sector, MSSM parameters must reproduce the correct mZ
• If terms on r.h.s. are not ~100 GeV, need cancellations to make thingswork. Fine-tuning !
• Calculate sensitivity to small changes in Lagrangian parameters:
• Add these in quadrature ! a measure of EWSB fine-tuning
• Can write the final expression as a function of mA, µ, tan ", mZ
• For tan " >> 1,
• Fine-tuned for large µ, to a smaller extent for small tan ", large mA.
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Our Approach
Work within (phenomenological) MSSM
Assume no relations between weak-scale MSSM parameters
No accidental cancellations
(ignore correlations that are true only on a measure zerohypersurface of the parameter space; want to make general
statements valid in most of the parameter space)
The lightest neutralino is dark matter, and makes up all of theobserved dark matter in the universe
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Dark Matter in the MSSM
• Neutralino mass matrix:
• The lightest neutralino (dark matter)
• The relative sizes of M1, M2, µ determine the contentof the LSP neutralino
Spin independent scattering(strongest bounds)
Spin independent scattering
Direct detection cross section depends only onIgnore this contribution
Spin independent scattering
Direct detection cross section depends only onIgnore this contribution
Both cross section and fine tuning determined by the same parameters!(Reminder: fine tuning depends on mA, µ, tan ")
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Aside: Why not do the same with LHC data?
“No” impact on fine-tuning!
(3rd generation squarks
enter at loop level, gluinos
only relevant at two loops)
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The Procedure
• Scan over parameters
• Fix Higgs mass at
mH=120 GeV
• Requirements:
neutralino LSP, charginos heavier than 100 GeV
• Scan with all real, positive parameters (will look at
cases with negative or complex parameters later)
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LSP Neutralino content
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Xenon100 results are forcing us into pure gaugino or
pure higgsino regions!
LSP Neutralino content
Content “purity”
Red: >0.2
Orange; 0.1-0.2
Green: 0.01-0.1
Cyan: 0.001-0.01
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Gaugino Dark Matter and Fine-Tuning
M1< µ or M2< µ
Can derive an approximate, analytic bound (for all
real, positive parameters):
For a given LSP mass, a lower cross
section requires greater fine-tuning!
Also see hep-ph/0606134
Makes sense: Smaller cross section ! purer gaugino LSP
! larger µ ! more severely fine-tuned
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Gaugino Dark Matter and Fine-Tuning
Red: MLSP > 1 TeV
Green: MLSP > 100 GeV
Cyan: MLSP > 10 GeV
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Gaugino Dark Matter and Fine-Tuning
• Current Xenon bound ! More than 10% fine-tuning above 70 GeV
• Xenon 1T will probe regions with fine-tuning down to percent level!
Fine-tuning: Red, green, cyan: >10,100,1000
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Higgsino Dark Matter
µ < M1, M2
Can keep µ small and avoid fine-tuning, but increase M1, M2 and
suppress direct detection cross section
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Higgsino Dark Matter
µ < M1, M2
Can keep µ small and avoid fine-tuning, but increase M1, M2 and
suppress direct detection cross section
Need additional constraint:
Invoke relic density!
Requirement: relic density equal/exceed observed relic density
(we are ignoring contributions from squarks, including them can lead to
larger annihilation cross sections and lower relic density)
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require relic density to equal/exceed observed relic density
! require MLSP ~ µ > TeV ! HUGE fine-tuning
Higgsino Dark Matter
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Higgsino Dark Matter
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Negative/Complex Parameters
(Choose basis where M1, M2 can be negative/complex)
• Cancellations between contributions possible,
aforementioned correlations no longer hold
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However, such cases themselves require parameters to be tuned to
achieve the right cancellation
Quantify this accidental cancellation in the
same way as fine-tuning in the EWSB sector:
Red, orange, green, cyan: log10# < -47,-46,-45, and above
Negative/Complex Parameters
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Red, orange, green: $acc > 30,10, <10
Negative/Complex Parameters
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Red, orange, green: $acc > 30,10, <10
Old analytic bound no
longer applicable
A modified bound is more
satisfactory but not absolute
Negative/Complex Parameters
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With (left) and without (right) points with accidental
cancellations in direct detection cross section
Negative/Complex Parameters
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Summary of MSSM implications
• Current Xenon100 bounds require pure gaugino or higgsino LSP
• Gaugino LSP: smaller direct detection cross sections correlate withstronger fine-tuning; current Xenon100 bounds already imply 10%or worse tuning for LSP heavier than 70 GeV
• Higgsino LSP: a mild relic density constraint already requires sub-percent level fine-tuning
• Xenon1T can probe regions with fine tuning down to percent level
• These statements apply in the most general MSSM, assuming onlythe absence of accidental cancellations
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However, MSSM already suffers from naturalness problems:
• µ problem
The natural value of µ is order Plank scale, NOT weak scale
• Non observation of Higgs at LEP II
Tree level prediction: mH < mZ
LEP II bound: mH > 114 GeV
Need to tune squark masses to get a large enough loop
correction to push mH above the LEP II bound
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These problems evaded in extended models of supersymmetry
A representative case: NMSSM
extend MSSM by a single gauge-singlet superfield S
• µ problem
Effective µ term of right order generated when scalar component
of S acquires a VEV of order SUSY breaking scale
• Non observation of Higgs at LEP II
Light Higgs with reduced couplings, can lie below the LEP II
experimental bound
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Additional field content in the NMSSM
• One additional neutralino: the singlino
mixes with the four MSSM neutralinos; dark matter can have
a singlino component
• One additional CP-even and one CP-odd neutral Higgs
boson
New channels available for scattering
• Direct detection picture can be very different!
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WORK IN PROGRESS…
Can we get small direct detection cross
sections without fine-tuning in the NMSSM?
BACKUP SLIDES
Direct Detection Cross Section
Spin independent, elastic DM-nucleon scattering at zero momentum exchange
Derivation: Analytic bound for gaugino dark matter
Since g’<g, assume bino dark matter: M1 << µ<< M2
Decoupling limit mA >> mZ
Large tan " limit
From the
resulting 3x3
matrix